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We are asked to find the remainder when the polynomial \( 6x^2 + 11x - 3 \) is divided by \( 2x - 1 \). To solve this, we can use polynomial division, or alternatively, synthetic division since the divisor is linear.

Let's perform synthetic division to find the remainder.

### Step 1: Set up for synthetic division
The divisor is \( 2x - 1 \). To set this up for synthetic division, we use \( \frac{1}{2} \) as the value to divide by.

The polynomial to divide is \( 6x^2 + 11x - 3 \), and we will apply synthetic division to find the remainder.

Let's calculate this.The remainder when the polynomial \( 6x^2 + 11x - 3 \) is divided by \( 2x - 1 \) is \( 4 \).

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How is polynomial division different from synthetic division?
2. Can synthetic division be used for divisors that are not linear?
3. What is the quotient when dividing \( 6x^2 + 11x - 3 \) by \( 2x - 1 \)?
4. How can the Remainder Theorem be applied in this case?
5. Can synthetic division be applied to polynomials with higher degrees?

**Tip:** Always verify the divisor's form before starting synthetic division. For \( ax - b \), use \( b/a \) as the divisor in the synthetic division process.

What is the remainder when the polynomial 6x^2 + 11x - 3 is divided by 2x - 1?

Learn how to find the remainder when dividing the polynomial 6x^2 + 11x - 3 by 2x - 1 using synthetic division. This problem demonstrates polynomial division techniques suitable for high school algebra students.

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